Title: Confirmatory factor analysis under violations of distributional and structural assumptions

Authors: Yanyun Yang; Xinya Liang

Addresses: Department of Educational Psychology and Learning Systems, Florida State University, Box 306-4453, Tallahassee, FL, 32306, USA ' Department of Educational Psychology and Learning Systems, Florida State University, Box 306-4453, Tallahassee, FL, 32306, USA

Abstract: This simulation study evaluated CFA model results under violations of both distributional and structural assumptions using maximum likelihood (ML), robust maximum likelihood (RML), and weighted least square (WLS) estimation methods. Design factors included model complexity, the degree of non-normality of factor and error scores, sample sizes, and model misspecifications. In total, 72 conditions were used for data generation. Results were evaluated by rejection rate based on the model chi-square tests, fit function, CFI, RMSEA, and parameter estimates. Findings from the simulation study suggested that CFA results were robust to moderate violation of the non-normality of both factor and error scores under ML and RML methods, however, the degree of non-normality of factor scores impacted both overall model fit indices and loading estimates under WLS, particularly when the models were mis-specified. In addition, correctly specified and mis-specified models were likely detected by combining results from multiple estimation methods.

Keywords: confirmatory factor analysis; CFA model results; distributional assumptions; structural assumptions; simulation; modelling; assumption violations.

DOI: 10.1504/IJQRE.2013.055642

International Journal of Quantitative Research in Education, 2013 Vol.1 No.1, pp.61 - 84

Received: 22 Nov 2012
Accepted: 21 Feb 2013
Published online: 29 Apr 2014 *

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